Solve (4,5*12/3-6,75)*2/3/(3frac{1{3}*0,3+51/3*frac{1}{8}):2frac{2}{3}}+frac{1frac{4}{11}*0,22:0,3-0,9}{(0,2-frac{3}{40})*1,6}

$$\frac { ( 4,5 \cdot 1 \frac { 2 } { 3 } - 6,75 ) \cdot \frac { 2 } { 3 } } { ( 3 \frac { 1 } { 3 } \cdot 0,3 + 5 \frac { 1 } { 3 } \cdot \frac { 1 } { 8 } ) : 2 \frac { 2 } { 3 } } + \frac { 1 \frac { 4 } { 11 } \cdot 0,22 : 0,3 - 0,9 } { ( 0,2 - \frac { 3 } { 40 } ) \cdot 1,6 }$$

Evaluate

$$1,3$$

Solution Steps

Multiply 1 and 3 to get 3.

$$\frac{\left(4,5\times \frac{3+2}{3}-6,75\right)\times \frac{2}{3}}{\frac{\frac{3\times 3+1}{3}\times 0,3+\frac{5\times 3+1}{3}\times \frac{1}{8}}{\frac{2\times 3+2}{3}}}+\frac{\frac{\frac{1\times 11+4}{11}\times 0,22}{0,3}-0,9}{\left(0,2-\frac{3}{40}\right)\times 1,6}$$

Add 3 and 2 to get 5.

$$\frac{\left(4,5\times \frac{5}{3}-6,75\right)\times \frac{2}{3}}{\frac{\frac{3\times 3+1}{3}\times 0,3+\frac{5\times 3+1}{3}\times \frac{1}{8}}{\frac{2\times 3+2}{3}}}+\frac{\frac{\frac{1\times 11+4}{11}\times 0,22}{0,3}-0,9}{\left(0,2-\frac{3}{40}\right)\times 1,6}$$

Convert decimal number 4,5 to fraction \frac{45}{10}. Reduce the fraction \frac{45}{10} to lowest terms by extracting and canceling out 5.

$$\frac{\left(\frac{9}{2}\times \frac{5}{3}-6,75\right)\times \frac{2}{3}}{\frac{\frac{3\times 3+1}{3}\times 0,3+\frac{5\times 3+1}{3}\times \frac{1}{8}}{\frac{2\times 3+2}{3}}}+\frac{\frac{\frac{1\times 11+4}{11}\times 0,22}{0,3}-0,9}{\left(0,2-\frac{3}{40}\right)\times 1,6}$$

Multiply \frac{9}{2} times \frac{5}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\left(\frac{9\times 5}{2\times 3}-6,75\right)\times \frac{2}{3}}{\frac{\frac{3\times 3+1}{3}\times 0,3+\frac{5\times 3+1}{3}\times \frac{1}{8}}{\frac{2\times 3+2}{3}}}+\frac{\frac{\frac{1\times 11+4}{11}\times 0,22}{0,3}-0,9}{\left(0,2-\frac{3}{40}\right)\times 1,6}$$

Do the multiplications in the fraction \frac{9\times 5}{2\times 3}.

$$\frac{\left(\frac{45}{6}-6,75\right)\times \frac{2}{3}}{\frac{\frac{3\times 3+1}{3}\times 0,3+\frac{5\times 3+1}{3}\times \frac{1}{8}}{\frac{2\times 3+2}{3}}}+\frac{\frac{\frac{1\times 11+4}{11}\times 0,22}{0,3}-0,9}{\left(0,2-\frac{3}{40}\right)\times 1,6}$$

Reduce the fraction \frac{45}{6} to lowest terms by extracting and canceling out 3.

$$\frac{\left(\frac{15}{2}-6,75\right)\times \frac{2}{3}}{\frac{\frac{3\times 3+1}{3}\times 0,3+\frac{5\times 3+1}{3}\times \frac{1}{8}}{\frac{2\times 3+2}{3}}}+\frac{\frac{\frac{1\times 11+4}{11}\times 0,22}{0,3}-0,9}{\left(0,2-\frac{3}{40}\right)\times 1,6}$$

Convert decimal number 6,75 to fraction \frac{675}{100}. Reduce the fraction \frac{675}{100} to lowest terms by extracting and canceling out 25.

$$\frac{\left(\frac{15}{2}-\frac{27}{4}\right)\times \frac{2}{3}}{\frac{\frac{3\times 3+1}{3}\times 0,3+\frac{5\times 3+1}{3}\times \frac{1}{8}}{\frac{2\times 3+2}{3}}}+\frac{\frac{\frac{1\times 11+4}{11}\times 0,22}{0,3}-0,9}{\left(0,2-\frac{3}{40}\right)\times 1,6}$$

Least common multiple of 2 and 4 is 4. Convert \frac{15}{2} and \frac{27}{4} to fractions with denominator 4.

$$\frac{\left(\frac{30}{4}-\frac{27}{4}\right)\times \frac{2}{3}}{\frac{\frac{3\times 3+1}{3}\times 0,3+\frac{5\times 3+1}{3}\times \frac{1}{8}}{\frac{2\times 3+2}{3}}}+\frac{\frac{\frac{1\times 11+4}{11}\times 0,22}{0,3}-0,9}{\left(0,2-\frac{3}{40}\right)\times 1,6}$$

Since \frac{30}{4} and \frac{27}{4} have the same denominator, subtract them by subtracting their numerators.

$$\frac{\frac{30-27}{4}\times \frac{2}{3}}{\frac{\frac{3\times 3+1}{3}\times 0,3+\frac{5\times 3+1}{3}\times \frac{1}{8}}{\frac{2\times 3+2}{3}}}+\frac{\frac{\frac{1\times 11+4}{11}\times 0,22}{0,3}-0,9}{\left(0,2-\frac{3}{40}\right)\times 1,6}$$

Subtract 27 from 30 to get 3.

$$\frac{\frac{3}{4}\times \frac{2}{3}}{\frac{\frac{3\times 3+1}{3}\times 0,3+\frac{5\times 3+1}{3}\times \frac{1}{8}}{\frac{2\times 3+2}{3}}}+\frac{\frac{\frac{1\times 11+4}{11}\times 0,22}{0,3}-0,9}{\left(0,2-\frac{3}{40}\right)\times 1,6}$$

Multiply \frac{3}{4} times \frac{2}{3} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{3\times 2}{4\times 3}}{\frac{\frac{3\times 3+1}{3}\times 0,3+\frac{5\times 3+1}{3}\times \frac{1}{8}}{\frac{2\times 3+2}{3}}}+\frac{\frac{\frac{1\times 11+4}{11}\times 0,22}{0,3}-0,9}{\left(0,2-\frac{3}{40}\right)\times 1,6}$$

Cancel out 3 in both numerator and denominator.

$$\frac{\frac{2}{4}}{\frac{\frac{3\times 3+1}{3}\times 0,3+\frac{5\times 3+1}{3}\times \frac{1}{8}}{\frac{2\times 3+2}{3}}}+\frac{\frac{\frac{1\times 11+4}{11}\times 0,22}{0,3}-0,9}{\left(0,2-\frac{3}{40}\right)\times 1,6}$$

Reduce the fraction \frac{2}{4} to lowest terms by extracting and canceling out 2.

$$\frac{\frac{1}{2}}{\frac{\frac{3\times 3+1}{3}\times 0,3+\frac{5\times 3+1}{3}\times \frac{1}{8}}{\frac{2\times 3+2}{3}}}+\frac{\frac{\frac{1\times 11+4}{11}\times 0,22}{0,3}-0,9}{\left(0,2-\frac{3}{40}\right)\times 1,6}$$

Multiply 3 and 3 to get 9.

$$\frac{\frac{1}{2}}{\frac{\frac{9+1}{3}\times 0,3+\frac{5\times 3+1}{3}\times \frac{1}{8}}{\frac{2\times 3+2}{3}}}+\frac{\frac{\frac{1\times 11+4}{11}\times 0,22}{0,3}-0,9}{\left(0,2-\frac{3}{40}\right)\times 1,6}$$

Add 9 and 1 to get 10.

$$\frac{\frac{1}{2}}{\frac{\frac{10}{3}\times 0,3+\frac{5\times 3+1}{3}\times \frac{1}{8}}{\frac{2\times 3+2}{3}}}+\frac{\frac{\frac{1\times 11+4}{11}\times 0,22}{0,3}-0,9}{\left(0,2-\frac{3}{40}\right)\times 1,6}$$

Convert decimal number 0,3 to fraction \frac{3}{10}.

$$\frac{\frac{1}{2}}{\frac{\frac{10}{3}\times \frac{3}{10}+\frac{5\times 3+1}{3}\times \frac{1}{8}}{\frac{2\times 3+2}{3}}}+\frac{\frac{\frac{1\times 11+4}{11}\times 0,22}{0,3}-0,9}{\left(0,2-\frac{3}{40}\right)\times 1,6}$$

Cancel out \frac{10}{3} and its reciprocal \frac{3}{10}.

$$\frac{\frac{1}{2}}{\frac{1+\frac{5\times 3+1}{3}\times \frac{1}{8}}{\frac{2\times 3+2}{3}}}+\frac{\frac{\frac{1\times 11+4}{11}\times 0,22}{0,3}-0,9}{\left(0,2-\frac{3}{40}\right)\times 1,6}$$

Multiply 5 and 3 to get 15.

$$\frac{\frac{1}{2}}{\frac{1+\frac{15+1}{3}\times \frac{1}{8}}{\frac{2\times 3+2}{3}}}+\frac{\frac{\frac{1\times 11+4}{11}\times 0,22}{0,3}-0,9}{\left(0,2-\frac{3}{40}\right)\times 1,6}$$

Add 15 and 1 to get 16.

$$\frac{\frac{1}{2}}{\frac{1+\frac{16}{3}\times \frac{1}{8}}{\frac{2\times 3+2}{3}}}+\frac{\frac{\frac{1\times 11+4}{11}\times 0,22}{0,3}-0,9}{\left(0,2-\frac{3}{40}\right)\times 1,6}$$

Multiply \frac{16}{3} times \frac{1}{8} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{1}{2}}{\frac{1+\frac{16\times 1}{3\times 8}}{\frac{2\times 3+2}{3}}}+\frac{\frac{\frac{1\times 11+4}{11}\times 0,22}{0,3}-0,9}{\left(0,2-\frac{3}{40}\right)\times 1,6}$$

Do the multiplications in the fraction \frac{16\times 1}{3\times 8}.

$$\frac{\frac{1}{2}}{\frac{1+\frac{16}{24}}{\frac{2\times 3+2}{3}}}+\frac{\frac{\frac{1\times 11+4}{11}\times 0,22}{0,3}-0,9}{\left(0,2-\frac{3}{40}\right)\times 1,6}$$

Reduce the fraction \frac{16}{24} to lowest terms by extracting and canceling out 8.

$$\frac{\frac{1}{2}}{\frac{1+\frac{2}{3}}{\frac{2\times 3+2}{3}}}+\frac{\frac{\frac{1\times 11+4}{11}\times 0,22}{0,3}-0,9}{\left(0,2-\frac{3}{40}\right)\times 1,6}$$

Convert 1 to fraction \frac{3}{3}.

$$\frac{\frac{1}{2}}{\frac{\frac{3}{3}+\frac{2}{3}}{\frac{2\times 3+2}{3}}}+\frac{\frac{\frac{1\times 11+4}{11}\times 0,22}{0,3}-0,9}{\left(0,2-\frac{3}{40}\right)\times 1,6}$$

Since \frac{3}{3} and \frac{2}{3} have the same denominator, add them by adding their numerators.

$$\frac{\frac{1}{2}}{\frac{\frac{3+2}{3}}{\frac{2\times 3+2}{3}}}+\frac{\frac{\frac{1\times 11+4}{11}\times 0,22}{0,3}-0,9}{\left(0,2-\frac{3}{40}\right)\times 1,6}$$

Add 3 and 2 to get 5.

$$\frac{\frac{1}{2}}{\frac{\frac{5}{3}}{\frac{2\times 3+2}{3}}}+\frac{\frac{\frac{1\times 11+4}{11}\times 0,22}{0,3}-0,9}{\left(0,2-\frac{3}{40}\right)\times 1,6}$$

Multiply 2 and 3 to get 6.

$$\frac{\frac{1}{2}}{\frac{\frac{5}{3}}{\frac{6+2}{3}}}+\frac{\frac{\frac{1\times 11+4}{11}\times 0,22}{0,3}-0,9}{\left(0,2-\frac{3}{40}\right)\times 1,6}$$

Add 6 and 2 to get 8.

$$\frac{\frac{1}{2}}{\frac{\frac{5}{3}}{\frac{8}{3}}}+\frac{\frac{\frac{1\times 11+4}{11}\times 0,22}{0,3}-0,9}{\left(0,2-\frac{3}{40}\right)\times 1,6}$$

Divide \frac{5}{3} by \frac{8}{3} by multiplying \frac{5}{3} by the reciprocal of \frac{8}{3}.

$$\frac{\frac{1}{2}}{\frac{5}{3}\times \frac{3}{8}}+\frac{\frac{\frac{1\times 11+4}{11}\times 0,22}{0,3}-0,9}{\left(0,2-\frac{3}{40}\right)\times 1,6}$$

Multiply \frac{5}{3} times \frac{3}{8} by multiplying numerator times numerator and denominator times denominator.

$$\frac{\frac{1}{2}}{\frac{5\times 3}{3\times 8}}+\frac{\frac{\frac{1\times 11+4}{11}\times 0,22}{0,3}-0,9}{\left(0,2-\frac{3}{40}\right)\times 1,6}$$

Cancel out 3 in both numerator and denominator.

$$\frac{\frac{1}{2}}{\frac{5}{8}}+\frac{\frac{\frac{1\times 11+4}{11}\times 0,22}{0,3}-0,9}{\left(0,2-\frac{3}{40}\right)\times 1,6}$$

Divide \frac{1}{2} by \frac{5}{8} by multiplying \frac{1}{2} by the reciprocal of \frac{5}{8}.

$$\frac{1}{2}\times \frac{8}{5}+\frac{\frac{\frac{1\times 11+4}{11}\times 0,22}{0,3}-0,9}{\left(0,2-\frac{3}{40}\right)\times 1,6}$$

Multiply \frac{1}{2} times \frac{8}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{1\times 8}{2\times 5}+\frac{\frac{\frac{1\times 11+4}{11}\times 0,22}{0,3}-0,9}{\left(0,2-\frac{3}{40}\right)\times 1,6}$$

Do the multiplications in the fraction \frac{1\times 8}{2\times 5}.

$$\frac{8}{10}+\frac{\frac{\frac{1\times 11+4}{11}\times 0,22}{0,3}-0,9}{\left(0,2-\frac{3}{40}\right)\times 1,6}$$

Reduce the fraction \frac{8}{10} to lowest terms by extracting and canceling out 2.

$$\frac{4}{5}+\frac{\frac{\frac{1\times 11+4}{11}\times 0,22}{0,3}-0,9}{\left(0,2-\frac{3}{40}\right)\times 1,6}$$

Multiply 1 and 11 to get 11.

$$\frac{4}{5}+\frac{\frac{\frac{11+4}{11}\times 0,22}{0,3}-0,9}{\left(0,2-\frac{3}{40}\right)\times 1,6}$$

Add 11 and 4 to get 15.

$$\frac{4}{5}+\frac{\frac{\frac{15}{11}\times 0,22}{0,3}-0,9}{\left(0,2-\frac{3}{40}\right)\times 1,6}$$

Convert decimal number 0,22 to fraction \frac{22}{100}. Reduce the fraction \frac{22}{100} to lowest terms by extracting and canceling out 2.

$$\frac{4}{5}+\frac{\frac{\frac{15}{11}\times \frac{11}{50}}{0,3}-0,9}{\left(0,2-\frac{3}{40}\right)\times 1,6}$$

Multiply \frac{15}{11} times \frac{11}{50} by multiplying numerator times numerator and denominator times denominator.

$$\frac{4}{5}+\frac{\frac{\frac{15\times 11}{11\times 50}}{0,3}-0,9}{\left(0,2-\frac{3}{40}\right)\times 1,6}$$

Cancel out 11 in both numerator and denominator.

$$\frac{4}{5}+\frac{\frac{\frac{15}{50}}{0,3}-0,9}{\left(0,2-\frac{3}{40}\right)\times 1,6}$$

Reduce the fraction \frac{15}{50} to lowest terms by extracting and canceling out 5.

$$\frac{4}{5}+\frac{\frac{\frac{3}{10}}{0,3}-0,9}{\left(0,2-\frac{3}{40}\right)\times 1,6}$$

Divide \frac{3}{10} by 0,3 to get 1.

$$\frac{4}{5}+\frac{1-0,9}{\left(0,2-\frac{3}{40}\right)\times 1,6}$$

Subtract 0,9 from 1 to get 0,1.

$$\frac{4}{5}+\frac{0,1}{\left(0,2-\frac{3}{40}\right)\times 1,6}$$

Convert decimal number 0,2 to fraction \frac{2}{10}. Reduce the fraction \frac{2}{10} to lowest terms by extracting and canceling out 2.

$$\frac{4}{5}+\frac{0,1}{\left(\frac{1}{5}-\frac{3}{40}\right)\times 1,6}$$

Least common multiple of 5 and 40 is 40. Convert \frac{1}{5} and \frac{3}{40} to fractions with denominator 40.

$$\frac{4}{5}+\frac{0,1}{\left(\frac{8}{40}-\frac{3}{40}\right)\times 1,6}$$

Since \frac{8}{40} and \frac{3}{40} have the same denominator, subtract them by subtracting their numerators.

$$\frac{4}{5}+\frac{0,1}{\frac{8-3}{40}\times 1,6}$$

Subtract 3 from 8 to get 5.

$$\frac{4}{5}+\frac{0,1}{\frac{5}{40}\times 1,6}$$

Reduce the fraction \frac{5}{40} to lowest terms by extracting and canceling out 5.

$$\frac{4}{5}+\frac{0,1}{\frac{1}{8}\times 1,6}$$

Convert decimal number 1,6 to fraction \frac{16}{10}. Reduce the fraction \frac{16}{10} to lowest terms by extracting and canceling out 2.

$$\frac{4}{5}+\frac{0,1}{\frac{1}{8}\times \frac{8}{5}}$$

Multiply \frac{1}{8} times \frac{8}{5} by multiplying numerator times numerator and denominator times denominator.

$$\frac{4}{5}+\frac{0,1}{\frac{1\times 8}{8\times 5}}$$

Cancel out 8 in both numerator and denominator.

$$\frac{4}{5}+\frac{0,1}{\frac{1}{5}}$$

Divide 0,1 by \frac{1}{5} by multiplying 0,1 by the reciprocal of \frac{1}{5}.

$$\frac{4}{5}+0,1\times 5$$

Multiply 0,1 and 5 to get 0,5.

$$\frac{4}{5}+0,5$$

Convert decimal number 0,5 to fraction \frac{5}{10}. Reduce the fraction \frac{5}{10} to lowest terms by extracting and canceling out 5.

$$\frac{4}{5}+\frac{1}{2}$$

Least common multiple of 5 and 2 is 10. Convert \frac{4}{5} and \frac{1}{2} to fractions with denominator 10.

$$\frac{8}{10}+\frac{5}{10}$$

Since \frac{8}{10} and \frac{5}{10} have the same denominator, add them by adding their numerators.

$$\frac{8+5}{10}$$

Add 8 and 5 to get 13.

$$\frac{13}{10}$$

Factor

$$\frac{13}{2 \cdot 5} = 1\frac{3}{10} = 1.3$$